LUCASVILLE, Ohio — A man who shot his wife to death because she wanted to leave him was executed Wednesday, the first Ohio inmate put to death using new injection guidelines adopted because the last execution was plagued with problems.

Rocky Barton was closely examined several times for suitable injection sites before he died at 10:27 a.m. at the Southern Ohio Correctional Facility.

Barton said he deserved to die and gave up his appeals that could have delayed his execution for years.

The state’s lethal injection protocol was changed after the execution of Joseph Clark in May, which was held up 90 minutes when prison staff struggled to find a viable vein and one they used collapsed.

The state now requires staff to make every effort to find two injection sites and use a new method to make sure the veins stay open once entryways are inserted.

The process appeared to go smoothly Wednesday, prisons Director Terry Collins said. Two injection sites were established — one as a backup in case something went wrong, he said.

The execution team appeared more relaxed and less hurried after the new guidelines advised staff against feeling pressured to follow what had become an artificial self-imposed time frame to complete an execution quickly, Collins said.

Previously, examinations of inmates before an execution consisted of a visual check and a review of his medical file, according to a June report by the Ohio Department of Rehabilitation and Correction.

Clark’s execution drew criticism from death penalty opponents who said the problems illustrated why the method of capital punishment is cruel and unconstitutional, and it came amid a growing national debate about lethal injection.

Barton, 49, was convicted of aggravated murder for the 2003 killing of Kimbirli Jo Barton, 44, at the couple’s home near Waynesville, about 35 miles northeast of Cincinnati. He has admitted shooting her after she told him she was leaving him.

In an interview last month, Barton said he wasn’t worried about the lethal injection method. “I got good veins,” he said.

In his final statement, Barton turned to his wife’s son and two daughters and said: “I’m sorry for what I done, sorry for killing your momma and for what I done to you.”